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On the expected complexity of the 3-dimensional Voronoi diagram



Javier Bernal


Let 5 be a set of n sites chosen independently from a uniform distribution in a cube in 3—dimensional Euclidean space. In this paper, work by Bentley, Weide and Yao is extended to show that the Voronoi diagram for 5 has an expected 0{n) number of faces. A consequence of the proof of this result is that the Voronoi diagram for 5 can be constructed in expected 0[n) time.
NIST Interagency/Internal Report (NISTIR) - 4321
Report Number


algorithm, computational geometry, expected complexity, expected linear, expected time analysis, Voronoi diagram


Bernal, J. (1990), On the expected complexity of the 3-dimensional Voronoi diagram, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 19, 2024)


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Created May 1, 1990, Updated November 10, 2018